One-dimensional Diffusion Flames Research Articles

Modeling of Sandia Flame D with the non-adiabatic chemistry tabulation approach: the effects of different laminar flames on NO X prediction.

The effects of different one-dimensional laminar flames on the prediction of nitrogen oxide (NO X ) emission in Sandia Flame D are numerically investigated using a flamelet method in the present work. In addition to the basic control variables of the mixture fraction and the reaction progress variable for chemistry tabulation in this combustion model, two additional variables of mixture fraction variance and enthalpy loss are added to the control variable space to improve prediction accuracy of the NO X pollutant. The former variable of mixture fraction variance is used for the presumed probability density function integration, and the latter takes into account the non-adiabatic effect. Two flamelet libraries are generated based on the one-dimensional unstretched premixed flame and the one-dimensional counterflow diffusion flame, respectively. An additional transport equation for the mass fraction of nitrogen oxide (NO) is solved for improving prediction accuracy. The unsteady Reynolds-averaged Navier-Stokes (URANS) simulation results are compared and analyzed with experimental data. The simulation results show dependence on the type of laminar flame. In the four-dimensional control variable space, the results with steady unstretched premixed flame indicate great agreement on the predictions of temperature and NO field. The computational method proposed in the present work sheds light on the high-precision combustion numerical simulation of NO X emission.

Simulation of high-pressure methane-oxygen combustion with a new reduced chemical mechanism

The modeling and simulation of methane-oxygen combustion at high pressure requires a dedicated kinetic mechanism to obtain a precise description of the fuel decomposition. However, using the detailed mechanisms literature in high-fidelity simulations, like direct numerical simulations, is not possible due to the high numerical cost. Accordingly, a reduced chemical mechanism is required, and the one proposed in this study contains 17 species and 44 reactions to encompass a very large range of pressure (P∈[1,100] bar) and equivalence ratio (ϕ∈[0.2,14]). The Optimized and Reduced Chemistry method, that is based on directed relation graph with error propagation, is applied to the RAMEC kinetic scheme, and validations are performed for a set of canonical test-cases: auto-ignition delay simulation, one-dimensional laminar premixed flame freely propagating and one-dimensional counterflow diffusion flame. A very good agreement is obtained by comparison with the RAMEC detailed mechanism. To further evaluate the ability of the reduced mechanism, a premixed flame expanding in a homogeneous isotropic turbulence at high pressure (P=56 bar) is performed. The temporal evolution of the flame front is detailed from its ignition, revealing the flame behavior and its interaction with turbulence. The new reduced chemical mechanism performs well with a relative error of 4% for the maximum of temperature at each time step and even less if the difference observed in the auto-ignition times between the two mechanisms is considered. Finally, a substantial gain is found when using the reduced scheme on three-dimensional cases, the simulations being 8 times faster than those using the detailed scheme. A dedicated post-processing tool based on the contour tracing labeling method is developed to measure the flame length.

Dynamics of diffusion flames in a very low strain rate flow field: from transient one-dimensional to stationary two-dimensional regime

The present work describes the transition of transient one-dimensional diffusion flame into a steady two-dimensional regime in a new flow field configuration. To that end, a cylindrical burner from which fuel is ejected radially and uniformly is positioned in the middle of two impinging flows. The chosen conditions are such that the strain rate is very low. The majority of the flame is located in a region of the flow field where spatial coordinates are scaled with the reciprocal of the square root of the strain rate, and the velocities are scaled with the square root of the strain rate. To simplify the model, a potential flow is assumed, with its results compared with those from a more detailed incompressible Navier–Stokes flow solution. The evolution of the flame is similar in both cases, which shows that the idealised potential flow describes well the flow field in such a geometry. Mixture fraction and excess enthalpy variables are employed to describe the infinitely fast chemical reaction, and therefore, fuel mass fraction, oxidiser mass fraction, and temperature fields. Results show that the initial flame displacement is controlled by the radial transport of fuel near the burner, where the impinging flows have a negligible influence. After that region, the flame is strongly influenced by the impinging flows where its acceleration is observed. Moreover, the proposed asymptotic solutions highlight the main transport mechanisms of reactants to the flame under different conditions and show the dependence of the flame on the chemical and flow field parameters. The stationary solution presents a diffusion flame with continuous geometric variation, from the counterflow to the coflow regime.

Single-Phase Instability in Non-Premixed Flames Under Liquid Rocket Engine Relevant Conditions

Under rocket-relevant conditions, real-gas effects and thermodynamic nonidealities are prominent features of the flow field. Experimental investigations indicate that phase separation can occur, depending on the operating conditions and on the involved species in the multicomponent flow. During the past decades, several research groups in the rocket combustion community have addressed this topic. In this contribution, a high-fidelity thermodynamic framework comprising real-gas and multicomponent phase-separation effects is employed to investigate liquid-oxygen/methane and liquid-oxygen/hydrogen flames at high pressure. A thorough introduction and discussion on multicomponent phase separation are conducted. The model is validated with experimental data and incorporated in a reacting flow computational fluid dynamics code. Using one-dimensional counterflow diffusion flames, the thermodynamic states and processes are discussed. Both real-gas and phase-separation effects are present and quantified in terms of derived properties. Finally, the method is applied in a three-dimensional Large-Eddy Simulation of a single-element reference test case, and the results are compared to experimental data.

Soot morphology and nanostructure in complex flame flow patterns via secondary particle surface growth

While the majority of studies explore soot formation in relatively simple, one-dimensional flames, most real-world flames consist of complex flows defined by large-scale turbulent eddies, recirculating flow patterns, and buoyancy effects. The effects of complex flow on soot physicochemical properties are poorly understood. This work employs an inverted gravity flame reactor (IGFR) to compare differences in soot growth between a one-dimensional laminar diffusion flame and a recirculating flame. Computational fluid dynamics (CFD) and experimental observations show particle oscillations between (i) a rich region with a high concentration of surface growth species, and (ii) a high-temperature oxidation region. Transmission electron microscopy (TEM) shows a significant difference in final primary particle diameter, where the one-dimensional flame produces primary particles 10–25 nm in diameter and the recirculating flame produces primary particles 25–75 nm in diameter. Additionally, larger primary particles from the recirculating flame contain both single and multiple cores. We propose that due to the spheroidal shape of the large primary particles, the secondary surface growth is primarily a result of polyaromatic hydrocarbon (PAH) condensation during re-entrainment of mature soot into the fuel-rich region followed by subsequent liquid layer carbonization in the high-temperature environment of the flame front. The recirculating flow patterns in the IGFR and repeated particle growth/oxidation cycle can serve as a model for soot formation in the large-scale flames with complex flow patterns, such as forest fires, coal fire plants, and other sources.

On formulating a simplified soot model for diesel and biodiesel combustion

In this study, a semi-empirical two-equation soot model that can predict soot in petrodiesel and biodiesel sprays and quantitative differences between soot volume fractions in the two sprays under engine conditions is developed. n-Heptane is used as the surrogate for petrodiesel and a ternary mixture of methyl decanoate, methyl-9-decanoate, and n-heptane as the surrogate for biodiesel. The n-heptane simulations are conducted using a 160-species mechanism. In the case of the ternary biodiesel surrogate, a 115-species reduced mechanism is employed to model the chemical kinetics. The semi-empirical soot model includes soot inception, surface growth, coagulation, and also oxidation. The results from the semi-empirical model will be compared to those obtained from a detailed soot kinetics model in one-dimensional diffusion flame studies. Analysis of the results shows that the model developed in this work can predict soot formation at various conditions for both petrodiesel and biodiesel fuels reasonably well, and at a fraction of the computational cost of the detailed soot kinetics mechanism.

H111 対向流プール燃焼を用いたエタノールの蒸発・燃焼過程に対する研究(一般講演(3))

For obtaining the data that contributes to propose detailed chemical reaction mechanism including the evaporation process of the liquid fuel, experimental study of counter-flow pool combustion was conducted. The one-dimensional diffusion flame was formed in this configuration. With respect to the counter-flow pool combustion of ethanol in this study, we carried out the temperature measurement by thermocouple and OH measurement by laser induced fluorescence method. The results obtained by the experiments were compared with the numerical simulation with OPPDIF/CHEMKIN-Pro. Results showed good agreement with experimental results and numerical results. In addition, we also tried numerical simulation of hydrazine as a realistic fuel.

Modeling CO2 Chemical Effects on CO Formation in Oxy-Fuel Diffusion Flames Using Detailed, Quasi-Global, and Global Reaction Mechanisms

Interest in oxy-fuel combustion as one of the leading carbon capture technologies has grown significantly in the past two decades. Experimental studies have shown higher CO concentration in oxy-fuel diffusion flames than in traditional air-fuel flames of both gaseous and solid fuels. The higher CO concentration changes the flame profiles, and it may have impacts on pollutants formation. This article presents a numerical study regarding the chemical effects of CO2 on CO formation in the flame region, and their modeling approaches in CFD simulations. Equilibrium calculation confirms higher CO concentration associated with fuel-rich stoichiometry in CO2 diluted combustion environment. One-dimensional counter-flow diffusion flame simulation using detailed reaction mechanisms reveals that the reaction enhances CO formation in the presence of high CO2 concentration, leading to a significantly higher CO concentration under oxy-fuel combustion conditions. High CO2 concentration also impacts the reaction via OH radical and results in lower H2 and higher H2O concentrations in the flame profile. Computational fluid dynamics (CFD) simulations of a swirling diffusion flame under air-fired and oxy-fuel conditions were conducted using the eddy dissipation model and the eddy dissipation concept model with quasi-global and global kinetic mechanisms. Results show that reasonable CO predictions can only be obtained using finite-rate approach with appropriate mechanisms considering the CO2 chemical effects. The Westbrook–Dryer two-step mechanism consistently underestimates the CO concentrations. In contrast, the Westbrook–Dryer multiple-step mechanism captures the chemical effects of CO2, and improves the predictions.

Correlation of optical emission and turbulent length scale in a coaxial jet diffusion flame

This article investigates the correlation between optical emission and turbulent length scale in a coaxial jet diffusion flame. To simulate the H2O emission from an H2/O2 diffusion flame, radiative transfer is calculated on flame data obtained by numerical simulation. H2O emission characteristics are examined for a one-dimensional opposed-flow diffusion flame. The results indicate that H2O emission intensity is linearly dependent on flame thickness. The simulation of H2O emission is then extended to an H2/O2 turbulent coaxial jet diffusion flame. Time series data for a turbulent diffusion flame are obtained by Large Eddy Simulation, and radiative transfer calculations are conducted on the LES results to simulate H2O emission optical images. The length scales of visible structures in the simulated emission images are determined by the procedure proposed by Ivancic and Mayer (2002) [8]. The length scales of emission intensity are compared with the integral length scales of velocity and temperature evaluated from LES flowfield data. The results clearly indicate that the length scale of emission intensity agrees well with the integral length scale of temperature, and is also close to that of the radial velocity component. Finally, the explanation as to why the integral length scale of temperature can be extracted from emission intensity distributions is stated.

Radiation enhanced B-Number

Radiative heat transfer plays a crucial role in most fire hazard related combustion processes. The existing classic and modified mass transfer B-Numbers have deficiencies for some burning cases of fires because they do not involve external radiation and/or assume flame transparent to thermal radiation. This study extended the concept of the mass transfer B-Number using the one-dimensional steady-state diffusion flame model. An analytical expression of the universal mass transfer B-Number BR was derived, which applies to semi-transparent flames with external radiation. Compared with the classic mass transfer B-Number, in the numerator denoting the net heat generated and held by the combustion system, BR has an additional term that represents radiative heat which is being held and transferred within the semi-transparent flame; as well as in the denominator denoting the convective heat needing for maintaining the combustion, the contribution from the radiative heat is deducted from the total heat required for vaporizing a unit mass of fuel at the fuel surface. BR increases as external radiation and/or ambient oxygen concentration raise. In order to examine its physical significance, new parameters were defined and illustrated, such as the mass transfer equivalent absorption coefficient, specific radiant heat feedback and radiation factor, that demonstrate interactions of heat and mass transfers and radiative absorption and emission within inhomogeneous flames. Effects of the external radiation and ambient oxygen concentration on these parameters were also evaluated. Increases in the radiation factor as the ambient oxygen concentration rises theoretically validated enhanced radiative heat transfer in rich oxygen combustion.

Modeling Combustion Reactions in a Diffusion Flame: Comparison between the Detailed-chemistry and Equilibrium Models

This paper discusses the validity of the mixture-fraction model with the assumption of chemical equilibrium, which is widely used to simulate a diffusion flame. Two equilibrium models were tested: (1) a single-step equilibrium model that considers only the fuel, oxygen, nitrogen, carbon dioxide, and water vapor; (2) a multi-step equilibrium model that considers 53 intermediate species. These equilibrium models were compared with the results of a detailed-chemistry model that considers the rates of 325 elementary reactions. The detailed-chemistry model was applied to one-dimensional counterflow diffusion flames. Temperature and mass fractions computed by the detailed-chemistry model were generally between the values given by the two equilibrium models. Depending on the condition and the range of mixture fraction, either a single-step equilibrium model or a multi-step equilibrium model better approximated the detailed-chemistry model. When the flame temperature was increased by using pure oxygen as the oxidizer, the multi-step equilibrium model tended to be more accurate than the single-step equilibrium model.

Experimental realization and characterization of unstretched planar one-dimensional diffusion flames

A burner configuration that allows the creation of nearly unstretched one-dimensional diffusion flames has recently been introduced. This paper presents the first detailed characterization of flames produced in such a burner to assess how well they approach the idealized one-dimensional configuration, which is used extensively for the development of theoretical models for diffusion flame stability. Particular emphasis is directed at quantifying the remaining inhomogeneities in the burner, such as residual flame stretch or variations in the boundary conditions, and identifying possible means to minimize them. Measurements made include the velocity field, stable species concentration profiles and temperature distribution throughout the burning chamber. Additionally, the flame position in the burner is determined as a function of mixture strength, reactant transport properties and bulk flow velocity. All the measurements are found to be in good agreement with a simplified one-dimensional flame model. However, the boundary conditions and their physical location have to be determined experimentally on both sides of the flame, which complicates comparison with results from theoretical and numerical models. Despite these limitations, we conclude that this new burner type provides a good experimental approximation of the one-dimensional idealized construct.

Thermal-diffusive instabilities in unstretched, planar diffusion flames

The recent development of a novel research burner at EPFL has opened the way for experimental investigations of essentially unstretched planar diffusion flames. In particular, it has become feasible to experimentally validate theoretical models for thermal-diffusive instabilities in idealized one-dimensional diffusion flames. In this paper, the instabilities observed close to the lean extinction limit are mapped in parameter space, notably as function of the two reactant Lewis numbers. Cellular and pulsating instabilities are found at low and high Lewis numbers, respectively, as predicted by linear stability analyses. The detailed investigation of these two types of instabilities reveals the dependence of cell size and pulsation frequency on the transport properties of the reactants and on flow conditions. The experimental scaling of the cell size is found in good agreement with linear stability. The comparison between experimental and theoretical pulsation frequencies, on the other hand, was hampered by the impossibility of experimentally reproducing the parameters of the stability calculations. Hence, a heuristic correlation between pulsation frequency and flow parameters, transport properties, in particular the Damköhler number, and oscillation amplitude has been developed and awaits theoretical interpretation.

Radiation blockage in small scale PMMA combustion

Fuel vapors, soot and products of combustion near a burning fuel surface often block much of the radiative heat feedback to the fuel surface of a burning object. The blockage phenomenon was clearly observed in experiments of small 9.5 cm diameter PMMA pool fires subjected to external radiation burning in ambient atmospheres of different oxygen concentrations. The measurements are explained by a one-dimensional model of a diffusion flame, which focuses on the radiant absorption and emission of the soot–gas mixture of the flame. An approximate Band Model was developed and inserted into Radcal to compute gas absorption and emission from MMA vapor, CO 2 and H 2O. The Radcal results are included in the one-dimensional diffusion flame model to provide a greater understanding of the radiation blockage and burning rates in various ambient atmospheres and externally imposed radiant heat fluxes. A comparison between experimental data and model prediction shows a good agreement.

Experiments in a novel quasi-1D diffusion flame with variable bulk flow

The novel species injector of a recently developed research burner, consisting of an array of hypodermic needles, which allows to produce quasi one-dimensional unstrained diffusion flames has been improved. It is used in a new symmetric design with fuel and oxidizer injected through needle arrays which allows to independently choose both the magnitude and direction of the bulk flow through the flame. A simplified theoretical model for the flame position with variable bulk flow is presented which accounts for the transport properties of both reactants. The model results are compared to experiments with a CO2-diluted H2-O2 flame and variable bulk flow. The mixture composition throughout the burning chamber is monitored by mass spectrometry. The resulting concentration profiles are also compared to the simplified theory and demonstrate that the new burner configuration produces a good approximation of the 1D chambered diffusion flame, which has been used extensively for the stability analysis of diffusion flames. Hence, the new research burner opens up new possibilities for the experimental validation of theoretical models developed in the idealized unstrained 1D chambered flame configuration, in particular models concerning the effect of bulk flow magnitude and direction on flame stability. Some preliminary results are presented on the effect of bulk flow direction on the thermal-diffusive cellular flame instability.

Analysis of high-pressure hydrogen, methane, and heptane laminar diffusion flames: Thermal diffusion factor modeling

Direct numerical simulations are conducted for one-dimensional laminar diffusion flames over a large range of pressures ( 1 ⩽ P 0 ⩽ 200 atm ) employing a detailed multicomponent transport model applicable to dense fluids. Reaction kinetics mechanisms including pressure dependencies and prior validations at both low and high pressures were selected and include a detailed 24-step, 12-species hydrogen mechanism (H 2/O 2 and H 2/air), and reduced mechanisms for methane (CH 4/air: 11 steps, 15 species) and heptane (C 7H 16/air: 13 steps, 17 species), all including thermal NO x chemistry. The governing equations are the fully compressible Navier–Stokes equations, coupled with the Peng–Robinson real fluid equation of state. A generalized multicomponent diffusion model derived from nonequilibrium thermodynamics and fluctuation theory is employed and includes both heat and mass transport in the presence of concentration, temperature, and pressure gradients (i.e., Dufour and Soret diffusion). Previously tested high-pressure mixture property models are employed for the viscosity, heat capacity, thermal conductivity, and mass diffusivities. Five models for high-pressure thermal diffusion coefficients related to Soret and Dufour cross-diffusion are first compared with experimental data over a wide range of pressures. Laminar flame simulations are then conducted for each of the four flames over a large range of pressures for all thermal diffusion coefficient models and results are compared with purely Fickian and Fourier diffusion simulations. The results reveal a considerable range in the influence of cross-diffusion predicted by the various models; however, the most plausible models show significant cross-diffusion effects, including reductions in the peak flame temperatures and minor species concentrations for all flames. These effects increase with pressure for both H 2 flames and for the C 7H 16 flames indicating the elevated importance of proper cross-diffusion modeling at large pressures. Cross-diffusion effects, while not negligible, were observed to be less significant in the CH 4 flames and to decrease with pressure. Deficiencies in the existing thermal diffusion coefficient models are discussed and future research directions suggested.

On molecular transport effects in real gas laminar diffusion flames at large pressure

Direct numerical simulations are conducted of unsteady, exothermic and one-dimensional laminar diffusion flames at large pressures. The simulations are used to assess the impact of molecular diffusion and real gas effects under high pressure conditions with simplified chemical kinetics. The formulation includes the fully compressible form of the governing equations, real gas effects modeled by the cubic Peng–Robinson equation of state, and a generalized form of the Soret and Dufour mass and heat diffusion vectors derived from nonequilibrium thermodynamics and fluctuation theory. The cross diffusion fluxes are derived for a ternary species system and include the effects of both heat and mass diffusion in the presence of temperature, concentration and pressure gradients (i.e., Soret and Dufour diffusion). The ternary species formulation is applied to a simplified single step reaction elucidating molecular and thermodynamic effects apparent in general combustion. Realistic models for pressure, temperature and species dependent heat capacities, viscosities, thermal conductivities and mass diffusivities are also included. Three different model reactions are simulated both including and neglecting Soret and Dufour cross diffusion. The simulation results show that Soret and Dufour effects are negligible for reactions comprised of species with equal or near equal molecular weights. However, Soret diffusion effects are apparent when species with nonequal molecular weights are involved in the reaction and result in reductions of the peak flame temperature. In addition, it is shown that neglect of cross diffusion leads to deviations in the predicted flame thicknesses, with under predictions for a hydrogen-oxygen system and over predictions for a heavy hydrocarbon reaction. These effects are explained in detail through examinations of the individual heat and mass flux vectors as well as through associated thermodynamic properties. A parametric study addresses the effects of the ambient pressure, the initial “flame Reynolds number,” the Damkohler number and the heat release parameter.

Stability of attached two-dimensional diffusion flame leading edges

This article examines the stability of a diffusion flame whose leading edge is located near the cold wall to which it attaches. Such leading edges appear in spreading flames, in burner and jet flames, and in flames burning over heterogeneous propellants. The flame model is idealized in order to facilitate analysis and interpretation. The method of analysis follows the examination of a one-dimensional diffusion flame by Vance et al. (2001, Combust. Theory Model. , 5 , 147). First, a basic state attached-flame problem is defined, which is subjected to small perturbations. The linearized disturbance equations are solved numerically to determine their eigenvalues, which indicate either stability or instability in response to infinitesimal perturbations of the basic state. Many of the one-dimensional model results of Vance et al. (2001) carry over to the two-dimensional case examined here. It is determined that the leading edge dictates the behavior of the remainder of the flame. In addition, the oscillation of the flame leading edge during both flame retreat and flame advance toward the stable position is examined.

Diffusion edge-flame: approximation of the flame tip Damköhler number

A relation is provided to approximate the Damköhler number at the tip of an edge-flame. The reaction zone extremity is modeled as a one-dimensional diffusion flame to which additional transverse fluxes are added. The Damköhler number at the flame tip is then characterized by a relation that involves the quenching Damköhler number of a one-dimensional diffusion flamelet. In this expression, a linear relation appears between the edge-flame Damköhler number and the amount of heat diffusing away from the flame tip, along the iso-mixture fraction surfaces. Numerical simulations are performed to estimate the validity of these analytical results. The behavior of the Damköhler number is well reproduced for a large range of two-dimensional and planar edge-flames, including weakly varying partially premixed fronts, triple-flames and edge-flames close to full quenching. The approximation is also verified in axi-symmetric lifted flames.

On the stability of one-dimensional diffusion flames established between plane, parallel, porous walls

A one-dimensional, non-premixed flame stability analysis is undertaken.Oscillatory and cellular flame instabilities are identified by a careful studyof the numerically calculated eigenvalues of the linearized system of equations. The numerical investigation details the critical locations for changes in flame behaviour, as well as the critical values of variousparameters that affect flame stability. A critical Lewis number, greaterthan unity, is identified as the value where unstable oscillations maybegin to appear (Le > Le c) and for which cellular flames can exist(Le < Le c). Some prior discussions are clarified regarding theaforementioned critical values, as well as the role of convection inproducing flame instabilities. The methodology of the stability analysis isdiscussed in detail.